Japan Radio Co. JLN-740A, Instruction Manual

Page: 226 / 232

C-2
Appendix C Error due to the deviation from
the irradiation angle reference value
2
Trim and heel
When there is a leaning of
δ
to the vertical line as shown in Figure 3, the Doppler shift frequency
that occurs to each of beam N
1
and beam N
2
is as follows:
f'
d1
= 2Vf
0
C (cos
θ
cos
δ
– sin
θ
sin
δ
)
f'
d2
= 2Vf
0
C (cos
θ
cos
δ
+ sin
θ
sin
δ
)
The error in the dual beams is:
ε
δ
= 100 (cos δ – 1) % (4)
The error in the single beam is:
ε '
δ
= 100 (cos δ + tan θ sin δ – 1) %
or
ε '
δ
= 100 (cos δ – tan θ sin δ – 1) % (5)
This shows that the error in dual beams is always a negative value regardless of the beam
irradiation angle.
When a slope of 5
° occurs, the error can be calculated as follows:
ε
δ
= - 0.38 %
ε '
δ
= -32.1 or –32.9 %
As shown above, the error of the dual beam system is smaller than that of the single beam
system, so that the dual beam system is more favorable.